Table of Gallons (fractions of) per foot of copper/pex?

I have a master bath addition that has a shower with a regular head and 3 body jets(2.5 gpm per).. the body jets have me looking to run a 3/4" hot and cold up to the shower.

Of course I always try to run the smallest available line so that the hot water takes the least amount of time to reach the fixture.

What I was wondering was where can I find information on what fraction of a gallon of water is in a foot of 3/4" copper or 3/4" pex.. What I am trying to figure out is if I run 3/4" copper up to this bath at 2.5 gpm (when I run the regular head only) how long is it going to take for the hot water to reach it.

I dont have that large of a run since the water heater is almost directly unde this bath two stores down.. The run could be as short as 20-25 feet but I still wanted to get an idea of how much stored cold water is in a foot of copper or better yet pex.

I didnt see a table like this in the code book, only miniumn sizes for certain fixture types.. I did some google searches but couldnt come up with anything.. I was just wondering on such a short run how much does pipe diameter effect the time it takes for the hot water to get there.

From another website.. inside diamter of 3/4" type L is .785.. so r is half that or .3925.. .3925*.3925*3.142 is an area of .484 sq inches, to get volume in inches per a foor of pipe multiple that by 12 get 5.8 cubic inches in a foot..

If you take 231 the number of cubic inches in a gallon and divide by 5.8 cubic inches in a foot you get 39.76 or almost 40 feet for pipe for a gallon of water..

If I can get there in 20 feet that is only .5 gallons of water that has to push its way out.. at 2.5 gallon per minute(assuming I run it full hot) that means .2 mintes or 12 seconds.. if I run 50%/50% hot cold it would be more like 24 seconds..

that is great news for me.. my current house has a tankless unit running 1/2 pipe up three stories.. takes forever for the unit to fire up and get my hot water.. If I do this with 3/8" pex to the faucet I will have hot water really fast.

Copper is a heat thief, so you need to know how much water will have to run just to heat the pipe so the water remains hot enough to use, not just how much water is in the pipe but 2-3-X pipe fulls 'til it's usable. Right? And that all depends on the temp of the water first drawn, the temp of the pipe and the degrees rise to usable water temp so the air temp around the bare copper etc. would all be required to even guess on how many gallons; or pipe fulls are needed/used/wasted or how many pennies were lost in heating the water etc..

Personally, instead of all this mental exercise..... I'd simply run 3/4" PEX and have it done by now. PEX is much more of an insulator than heat sink.